To solve the equation \( 3^{-2x+1} \cdot 3^{-2x-3} = 3^{-3} \), we can first simplify the left side using the properties of exponents:
\[ 3^{-2x+1} \cdot 3^{-2x-3} = 3^{(-2x+1) + (-2x-3)} = 3^{-4x - 2} \]
Thus, the equation becomes:
\[ 3^{-4x - 2} = 3^{-3} \]
Since the bases are the same, we can set the exponents equal to each other:
\[ -4x - 2 = -3 \]
Now, solve for \( x \):
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Add 2 to both sides: \[ -4x = -3 + 2 \] \[ -4x = -1 \]
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Divide by -4: \[ x = \frac{-1}{-4} = \frac{1}{4} \]
So, the solution for \( x \) is:
\[ \boxed{\frac{1}{4}} \] Thus, Esmeralda should select \( \frac{1}{4} \) as her answer.